where \(\Pi _{\mathcal {X}}(y)\)  denotes the Euclidean projection of the vector \(y\)  onto the set \(\mathcal {X}\) . The gradient mapping is a classical measure has been widely used in the literature as a convergence criterion when solving nonconvex constrained problems [1]}. It plays an analogous role of the gradient for constrained optimization problems; in fact when the set \(\mathcal {X}\equiv \mathbb {R}^d\)  the gradient mapping just reduces to \(\nabla F(\bar{x})\) . It should be emphasized that while the gradient mapping cannot be computed in the stochastic setting, it still serves as a measure of convergence. Our main goal in this work is to find an \(\epsilon \) -stationary solution to (REF ), in the sense described below.
